Chapter VI.
The Quinary System.
The origin of the quinary mode of counting has been discussed with some fulness in a preceding chapter, and upon that question but little more need be said. It is the first of the natural systems. When the savage has finished his count of the fingers of a single hand, he has reached this natural number base. At this point he ceases to use simple numbers, and begins the process of compounding. By some one of the numerous methods illustrated in earlier chapters, he passes from 5 to 10, using here the fingers of his second hand. He now has two fives; and, just as we say “twenty,” i.e. two tens, he says “two hands,” “the second hand finished,” “all the fingers,” “the fingers of both hands,” “all the fingers come to an end,” or, much more rarely, “one man.” That is, he is, in one of the many ways at his command, saying “two fives.” At 15 he has “three hands” or “one foot”; and at 20 he pauses with “four hands,” “hands and feet,” “both feet,” “all the fingers of hands and feet,” “hands and feet finished,” or, more probably, “one man.” All these modes of expression are strictly natural, and all have been found in the number scales which were, and in many cases still are, in daily use among the uncivilized races of mankind.
In its structure the quinary is the simplest, the most primitive, of the natural systems. Its base is almost always expressed by a word meaning “hand,” or by some equivalent circumlocution, and its digital origin is usually traced without difficulty. A consistent formation would require the expression of 10 by some phrase meaning “two fives,” 15 by “three fives,” etc. Such a scale is the one obtained from the Betoya language, already mentioned in Chapter III., where the formation of the numerals is purely quinary, as the following indicate:[227]
| 5. | teente | = 1 hand. |
| 10. | cayaente, or caya huena | = 2 hands. |
| 15. | toazumba-ente | = 3 hands. |
| 20. | caesa-ente | = 4 hands. |
The same formation appears, with greater or less distinctness, in many of the quinary scales already quoted, and in many more of which mention might be made. Collecting the significant numerals from a few such scales, and tabulating them for the sake of convenience of comparison, we see this point clearly illustrated by the following:
| 5. | amnaitone | = 1 hand. |
| 10. | amna atse ponare | = 2 hands. |
| 5. | abba tekkabe | = 1 hand. |
| 10. | biamantekkabe | = 2 hands. |
| 5. | alacötegladu | = 1 hand. |
| 10. | catögladu | = 2 hands. |
Niam Niam| 5. | biswe |
| 10. | bauwe | = 2d 5. |